Linear subspaces, symbolic powers and Nagata type conjectures

By Marcin Dumnicki, Brian Harbourne, Tomasz Szemberg, Halszka Tutaj-Gasi'nska. 2012

69 citations recorded by the source corpus.

Abstract Inspired by results of Guardo, Van Tuyl and the second author for lines in P 3 , we develop asymptotic upper bounds for the least degree of a homogeneous form vanishing to order at least m on a union of disjoint r-dimensional planes in P n for n ⩾ 2 r + 1 . These considerations lead to new conjectures that suggest that the well known conjecture of Nagata for points in P 2 is not an exotic statement but rather a manifestation of a much more general phenomenon which seems to have been overlooked so far.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4d90fb182ee8224e81821a8603f6bff5f6ec226a

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In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

The Waldschmidt constant for squarefree monomial ideals (2015, background): “eal deﬁning a ﬁnite sets of points in P1 ×P1 in [1]. Guardo et. al [17] also computed bα(I) when I is the ideal of general sets of points in P1 ×P1. In addition, upper bounds on bα(I) were studied in [9, 16], along with connections to Nagata’s conjecture. Even though computing bα(I) may be easier th”